The number of Internet host computers (computers connected directly to the Internet, for networks, bulletin boards, or online services) has been growing at the rate of f(x) = xe^(0.1x) million per year, where x is the number of years since 1990. Find the total number of Internet host computers added during the years 1990–2010.

Question

I don't know how to start this problem. Do I plug the f(x) inside the graph and do I check the years from 1990-2010 in the table? I assume it would be from 0-20 on the table. Can anyone help me on this? I think that's what might happen, but I am not sure.

Thanks again!

Answer 1

sounds like you want

f'(x) = x e^(.01x)

since you say that's the growth rate.

So, the total number of computers for 20 years is the integral from 0 to 20 of f'(x) dx

To do the integral, use integration by parts.